The Case for Assessing Quantitative Reasoning in Student Writing

"As in book literacy, evidence of students' ability to play the messy game of the [quantitative reasoning] discipline depends on seeing whether they can handle tasks without specific cues, prompts, or simplifying scaffolds from the teacher-coach or test designer."-Grant Wiggins, "'Get Real!': Assessing for Quantitative Literacy" inQuantitative Literacy: Why Numeracy Matters for Schools and Colleges

The very nature of QR presents challenges for traditional curricular reform and assessment strategies. The literature identifiesfour facets of QR.

First, effective implementation of QR requires abasic skill set.Without a nuanced understanding of basic mathematical concepts like ratios, percentages, and averages it is impossible to apply that quantitative knowledge with a high degree of sophistication. This understanding includes an appreciation for both the power and pitfalls of various QR tools.

Second, unlike traditional mathematics, which is intentionally abstract, QR explicitly requires that these skills beimplemented in context(De Lange 2003 p. 80, Richardson and McCallum 2003 p. 100-102, Steen 2004 p. 9-10, Bok 2006 p. 129). As Steen writes, "The test of numeracy, as of any literacy, is whether a person naturally uses appropriate skills in many different contexts" (2001 p. 6). Contextualized problem-solving requires students to engage in intellectual transference, applying lessons learned in one setting to a newly discovered problem. To teach QR in context, effective programs must "permeate the curriculum, not only in the sciences but also in the social sciences and, in appropriate cases, in the humanities" (Bok 2006 p. 134).

Third, students must learn tocommunicatecontextualized applications of QR (De Lange 2003 p. 77, Brakke 2003 p. 168). This includes visual presentation through tables and figures in addition to writing with numbers.

Finally, even students with the ability to communicate quantitative evidence in context must acquire thehabit of mindto approach questions with a quantitative lens (Steen 2001 p. 5, Hughes-Hallett 2003 p. 91, Steen 2004 p. 16-17). Steen argues that students "need a predisposition to look at the work through mathematical eyes" (2001 p. 2).

The multi-disciplinary, contextual character of QR often confounds efforts to create effective QR programs. As Steen (2004) points out, "Curricular talk tends to be dominated by disciplines....With no discipline naturally exercising leadership, there is neither an insistent nor a consistent call to make [QR] a priority of education at the college level" (p. 13-15). Even when a group of faculty members drawn from across the disciplines overcome institutional barriers and agree to prioritize QR instruction, it can be very difficult to devise a program which truly infuses the curriculum.

Some educators have responded to this challenge by rethinking the nature of standardized testing, creating context-rich test questions. Through short-answer essays, such tests may detect fluency in writing with numbers but do not permit students the time, space, or capacity to demonstrate the ability to choose wisely between graphical, tabular, and textual presentation.

What is much more important, QR problems in the real world are inherently ill-structured-ill-defined in some cases. In Wiggins' words, "As in book literacy, evidence of students' ability to play the messy game of the [QR] discipline depends on seeing whether they can handle tasks without specific cues, prompts, or simplifying scaffolds from the teacher-coach or test designer" (2003 p. 134 emphasis added). Because standardized QR tests clearly prompt students to apply a quantitative lens, such tests are inherently unable to assess students' propensity to consider voluntarily the quantitative facets of problems.

Given the cross-disciplinary nature of QR, only an equallycross-disciplinary assessmentstrategy can fully measure our effectiveness. As Steen (2004 p. 18) writes, "The interdisciplinary and contextual nature of [QR] cries out for a cross cutting approach." With student work drawn from courses taught by 197 different professors (Carleton has 170 FTE), Carleton's writing portfolio truly represents student thinking across the curriculum.

Moreover, the application of QR skills in student papers provides an inherentlycontext-rich environmentin which to assess proficiency.

Of particular value, writing assessment reveals as much about students' abilities to create tables and charts as to read them. While students may capably interpret charts and tables made by others, highly effective presentation skills only develop with practice (Miller 2004 p. 5). Most importantly, portfolio assessment providesinsight into students' habits of mindconcerning the power of quantitative evidence: because papers often do not explicitly require quantitative evidence we are able to determine whether students reflexively consider numerical facets of problems they face.

De Lange, Jan. 2003. "Mathematics for Literacy," inQuantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

Hughes-Hallett, Deborah. 2003. "The Role of Mathematics Courses in the Development of Quantitative Literacy" inQuantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.

Richardson, Randall M. and William G. McCallum. 2003. "The Third R in Literacy" ," inQuantitative Literacy: Why Numeracy Matters for Schools and Colleges, Bernard L. Madison and Lynn Arthur Steen, eds. Princeton, NJ: National Council on Education and the Disciplines.